Need clarification - Statistics

In mean computation from histogram topic , what happen if we consider a interval which has more frequency with almost same value
Example - In Sachin’s score data 10-20 interval has 59 frequency
If all 59 occurrences has value as either 11 or 19 then there will be high difference between approximate sum and actual sum

Actual sum [ when all 11] - 649
Actual sum [ when all 19] - 1121
Approximate sum [ 14.5 * 59] - 855.5

Kindly explain if this is special scenario to be handled in different approach.

Yes you’re right… What we can do here is to manage bin size accordingly, as per our requirements for the task.
In this particular case, please note that we want to estimate a mean value of whole population, with least error possible.